Known methods for generating tooth surfaces in bevel and hypoid gears are based on a concept of a tool together with its relative motions with respect to a work gear representing a "theoretical generating gear" rolling through mesh with the work gear. Working surfaces of the tool represent tooth surfaces of the theoretical generating gear, and known bevel and hypoid gear generating machines provide for positioning the tool and the work gear with respect to a machine axis (e.g., machine cradle axis) representing an axis of the theoretical generating gear. The working surfaces of the tool are rotated about the machine axis in a timed relationship with rotation of the work gear about its axis as though the working surfaces of the tool were the actual surfaces of another gear rotating through mesh with the work gear.
Most explanations of bevel and hypoid gear generation recount a principle that if tooth surfaces of the members of a bevel or hypoid gear pair are separately generated by rolling the respective members in mesh with "complementary" theoretical generating gears, tooth surfaces of the respective members will be generated conjugate to each other (i.e., fully mesh with each other). In accordance with this principle, complementary theoretical generating gears are understood to share the same axis and tooth surfaces, opposite sides of which constitute the respective tooth surfaces of the complementary gears.
Although most explanations of bevel and hypoid gear generation emphasize only the condition of complementarity, it is also known that complementarity alone is not a sufficient condition for generating conjugate tooth surfaces in mating gears. That is, the condition of complementarity must be combined with other conditions defining the theoretical generating gears as so-called "basic members." Two conditions must be fulfilled for a theoretical generating gear to meet the requirements of a basic member. First, relative angular velocity between the theoretical generating gear and either member of a conjugate gear pair must define an instant axis of rotation coincident with an instant axis of rotation defined by relative rotation of the conjugate gear pair. Second, relative linear velocity of points along the instant axis between the theoretical generating gear and either member of the conjugate gear pair must be in a ratio with the magnitude of the relative angular velocity matching a similar ratio of linear and angular velocity between the conjugate gear pair. In other words, the theoretical generating gear together with either member of a conjugate work gear pair must define the same "lead" (i.e., axial advance per radian of turning about the instant axis) as the conjugate gear pair. A more detailed explanation of basic members is found in U.S. Pat. No. 1,676,371 to Wildhaber.
In the case of a conjugate bevel gear pair, the magnitude of relative linear velocity along the instant axis between the gear pair is zero. Accordingly, it is possible to define a basic member of the pair as another bevel gear. Most explanations of bevel and hypoid gear generation depict tools arranged to represent complementary theoretical generating gears in the form of complementary crown gears (i.e., bevel gears having planer pitch surfaces perpendicular to their respective axes of rotation).
However, a basic member of a conjugate hypoid gear pair (other than one member or the other of the pair) is neither a bevel gear nor another hypoid gear. Hypoid gear pairs include axes which are offset with respect to each other resulting in a measure of relative linear velocity along the instant axis of the pair. Any basic member other than one or the other members of the gear pair must include a supplemental component of linear velocity in addition to the linear and angular velocities resulting from rotation about its axis. Typically, the basic member of a hypoid gear pair is considered as a helicoidal segment which includes a translating motion along its axis timed with rotation about its axis.
However, many bevel and hypoid gear pairs are understood to be manufactured according to a process in which the basic member is defined as being one of the members of the work gear pair. For example, according to U.S. Pat. No. 1,622,555 to Wildhaber, tooth surfaces of the larger member of the pair (usually a ring gear) are formed by the working surfaces of a tool without any generating motion between the tool and work gear. In other words, tooth surfaces of the ring gear member of the pair are formed as complementary surfaces of the tool. Tooth surfaces of the other member of the work gear pair (usually a pinion) are generated by a second tool arranged to represent the ring gear member. Thus, the working surfaces of the tool for generating the pinion tooth surfaces represent the actual tooth surfaces of the ring gear as a basic member of the work gear pair.
In practice, however, most tools used to generate mating gear pairs represent tooth surfaces of theoretical generating gears that depart slightly from complementarity. Some of this departure is desirable for producing a controlled amount of mismatch between otherwise conjugate mating members. Mismatch between mating tooth surfaces is provided to accommodate tooth distortions under expected loads and to permit some adjustability of the mounting locations of the gear members. However, other types of departure from complementarity are generally undesirable. For example, tooling limitations often preclude an exact representation of the desired tooth surfaces of theoretical generating gears.
Two main types of tooling are known for generating tooth surfaces in bevel and hypoid gears, namely, face milling tools and face hobbing tools. Face milling types of tooling have inherent characteristics which make representations of fully complementary tooth surfaces difficult. Face hobbing types of tooling may be easily arranged to represent complementary tooth surfaces but encounter problems in representing tooth surfaces which depart from complementarity for producing desirable mismatch between mating work gear tooth surfaces.
The two tooling types are associated with different machine operations. For example, face milling tools are used in intermittent indexing operations in which each tooth space in a work gear is separately generated. The work gear is indexed a predetermined amount about its axis between generating operations so that the generated tooth spaces are evenly distributed about the periphery of the work gear. In contrast, face hobbing tools are used in continuous indexing operations in which all of the tooth spaces in a work gear are formed by a single continuous generating motion. Continuous indexing operations require the tool and work gear to be rotated about their respective axes in a ratio of rotational speeds which enables different portions of the tool to engage successive tooth spaces in the work gear. The continuous indexing operation is performed at a much higher rate than the generating operation so that substantially the same tooth surfaces are generated in each tooth space.
Of the two types of tooling mentioned above, face milling tools have been by far the most common type of tooling by which bevel and hypoid gear tooth surfaces have been generated. Three main reasons may be supposed for this. First, intermittent indexing operations may be performed on a less complex machine than continuous indexing operations. Second, face milling tools are less complex and easier to manufacture and assemble than face hobbing tools. Third, tools having a similar shape to face milling tools (e.g., cup-shaped grinding wheels) may be used to finish grind tooth surfaces, whereas no corresponding form of face hobbing tool for finish grinding tooth surfaces has been commercially successful.
Face milling tools include a plurality of blades projecting from a front face of a cutter head which are arranged in one or more concentric circles about an axis of rotation of the cutter head. Typically, a set of "inside" blades for working convex flanks of work gear teeth are arranged at a first radius from the cutter head axis, and a set of "outside" blades for working concave flanks within the same tooth space are arranged at a second larger radius. The respective blades include cutting edges which are inclined at respective pressure angles to the axis of the cutter head. Rotation of the respective cutting edges about the axis of the cutter head defines respective working surfaces of the tool substantially in the form of conical surfaces of revolution.
However, such surfaces of revolution are not well suited to exactly representing complementary tooth surfaces of theoretical generating gears. By way of example, a pair of identical face milling tools may be considered to represent respective tooth surfaces of a pair of bevel crown gears. Although identical teeth may be represented in the crown gears, the condition of complementarity requires that the teeth of one member of a complementary pair exactly match the tooth spaces of the other member. In other words, the concave tooth flanks of the one member must match the convex tooth flanks of the other member and visa versa. However, in the identical cutter heads, the concave tooth flanks of both members are formed by outside blades at a larger radius than the radius of the inside blades for forming the convex tooth flanks of the same members. Thus, the longitudinal tooth curvatures of the mating concave and convex flanks of the crown gear pair represented by the identical face milling tools may be understood to depart from complementarity.
A second type of departure from complementarity relates to the working surfaces of opposite tooth flanks being arranged as concentric surfaces of revolution in the face milling tools. The concentric working surfaces of each of the identical tools define substantially parallel longitudinal tooth curves in each of the respective crown gears. However, longitudinal tooth curves of the respective flanks of tooth spaces in the crown gears depart from parallel by the angular spacing between gear teeth. Thus, the longitudinal tooth curves of the mating concave and convex flanks of the crown gear pair also depart from complementarity in angular orientation (i.e., spiral angle).
Of course, the just-explained characteristics of face milling tools have been long known, and methods to work with these characteristics have been developed in the art. For example, it has been known to match the longitudinal tooth curves formed in one member of a gear pair by using separate cutter heads having only inside or outside blades for working opposite tooth flanks in the mating gear member. It is also known from U.S. Pat. No. 1,676,371 to Wildhaber to rearrange the inside and outside blades of a complementary cutter head (referred to as a "straddle" cutter head) to work opposite flanks of the same work gear tooth instead of the opposite flanks of a tooth space. Other known methods relate to finding angular orientations between the axes of respective face milling tools to appropriately match longitudinal tooth curvatures as well as spiral angles at a mean point of contact between theoretical generating gears. For example, it is known from U.S. Pat. No. 1,654,199 to Wildhaber to relatively incline the tool axes about a longitudinal tangent line at a mean point of the respective tooth curves to appropriately match longitudinal curvatures between theoretical generating gears. It is also known to relatively incline the tool axes in directions which produce tapering width and depth teeth to appropriately match the spiral angles of theoretical generating gear tooth flanks at the selected mean points. The latter mentioned tool axes inclinations are almost universally practiced with face milling tools to provide for balancing tooth shape between mating work gear members.
Although the known methods to deal with the problems of longitudinal tooth curvature and spiral angle may be used to appropriately match theoretical generating gear tooth surfaces in the vicinity of a mean point between the surfaces, the represented tooth surfaces tend to depart from complementarity with increasing distance from the mean point at which the surfaces are matched. Often, these departures are not consistent with a desired mismatch between the mating work gear members. Accordingly, the art also includes a number of solutions for minimizing the residual effects of the solutions for at least approximately matching longitudinal curvatures and spiral angles of theoretical generating gear teeth.
Typically, these residual effects are measured by resulting contact characteristics between the mating work gears. In other words, once the gross shapes of the mating work gear tooth surfaces have been determined, further details of the tooth shapes are not so important as contact characteristics between the members which result from the difference or mismatch between the mating tooth surfaces. Thus, the residual effects of the corrections for tooth curvature and orientation are often related in terms of contact characteristics such as "bias bearing" (a contact pattern extending diagonally of mating tooth surfaces), "lame bearing" (a contact pattern higher on the tooth profile of one flank than the other), and "cross bearing" (contact patterns shifted to opposite ends of the tooth flanks).
Although face hobbing tools may be easily arranged to represent complementary generating gears, the same types of residual effects often occur as a result of modifications to the face hobbing tooling for producing desirable mismatch between mating gear members. Most known solutions for minimizing undesirable residual effects on tooth contact characteristics arising from the use of either face milling or face hobbing tooling relate to changing the respective definitions of the theoretical generating gears for producing mating gear members. In other words, the theoretical generating gears for generating tooth spaces in mating members of a work gear pair are defined in ways which depart from the requirements of substantially complementary basic members.
Accordingly, it may be understood that the known practices of generating bevel and hypoid gears, often deviate from the conventional explanation of bevel and hypoid gear generation. Once the tooth surfaces of a work gear member are defined, the tooth surfaces of that member may be generated by a tool arranged to represent any conjugate mating member. In other words, as long as respective theoretical generating gears define tooth surfaces which are conjugate to the desired tooth surfaces of the members of a work gear pair, it is not necessary for the theoretical generating gears to be complementary basic members or even conjugate to each other.
For example, U.S. Pat. No. 1,685,442 to Wildhaber discloses a method of eliminating the residual condition of "bias bearing" resulting from tool axis inclinations for producing tapering width and depth teeth. According to the known method, tooth flanks of a ring gear member of a work gear pair are generated in a customary manner conjugate to a nominal crown gear, and opposite flanks of the pinion member are separately generated by theoretical generating gears in the form of crown gears that are offset with respect to both the nominal crown gear and each other. The theoretical generating gears are also rotated together with the pinion member at different ratios of rotational speeds (i.e., different rates of generating roll). This is referred to as "modified roll".
U.S. Pat. No. 1,982,036 to Wildhaber extends the just-above described method to the more common practice of generating only one member (e.g., pinion) of a pair substantially conjugate to the non-generated tooth surfaces of the other member (e.g., ring gear) of the pair. Respective tooth surfaces of the pinion member are generated conjugate to theoretical generating gears which differ from the ring gear member to compensate for tooling limitations which preclude an exact representation of tooth surfaces of the ring gear member.
In addition to defining different locations and rotational speeds between theoretical generating gears for generating the respective members of a work gear pair, it is also known to define different motions along the respective axes of the theoretical generating gears. For example, U.S. Pat. No. 1,980,365 to Wildhaber discloses use of a translating motion of a theoretical generating gear along its axis timed with its rotation. This motion is also known as "helical motion". The translating motion defines one of the theoretical generating gears as a helicoidal segment, which is the basic generating member of a hypoid gear set, for simultaneously eliminating the "bias bearing" condition on both flanks of a gear member using the same ratio of generating roll.
Other motions affecting the generation of bevel and hypoid tooth surfaces are known, but these motions are mainly used to overcome machine limitations (as opposed to tool limitations) for appropriately representing a desired theoretical generating gear. For example, some bevel and hypoid gear generating machines are built without a provision for inclining the tool axis with respect to the machine axis (cradle axis) representing the axis of the theoretical generating gear. U.S. Pat. No. 2,310,484 to Wildhaber discloses a method of compensating for this machine limitation by modifying the rate of the generating roll in the course of generation to approximate motion about an axis of a theoretical generating gear that is inclined to the axis of the tool. This method is also known as "modified roll" In U.S. Pat. No. 2,773,429 to Wildhaber, a linear oscillating motion along the machine axis timed with generating roll is used for substantially the same purpose. Finally, it is known from U.S. Pat. No. 2,824,498 to Baxter et al. and a publication by Baxter entitled "An Application of Kinematics and Vector Analysis to the Design of a Bevel-Gear Grinder", American Society of Mechanical Engineers, 1964, to relatively translate the work gear in a direction substantially perpendicular to the machine cradle axis timed with generating roll to emulate a large crown gear and therefore enabling the formation of low shaft angle gears. This motion is also referred to as "vertical motion".
In view of the above discussion, it may now be appreciated that most of the fundamental teachings in the art of conventional bevel and hypoid gear generation may be attributed to the work of one inventor, Ernest Wildhaber, and most of that work was accomplished over thirty years ago. Since that time, the most important methodological advances in the art of bevel and hypoid gear generation have related to improved procedures for determining appropriate machine settings based upon Mr. Wildhaber's earlier work. The process by which machine settings are determined to produce acceptable tooth contact characteristics in work gears is known in the art as "development". Today, computer programs are used in the development process to take best advantage of the known possibilities for setting up bevel and hypoid gear generating machines to represent various theoretical generating gears.
Despite the availability of computer processing techniques and the long familiarity in the art with the effects of various representations of theoretical generating gears, it is often not possible to develop mating tooth surfaces with the exact contact characteristics that may be desired. Although it is usually possible to develop tooth contact characteristics which are at least marginally satisfactory, results are inconsistent from one job to the next.
Until recently, most bevel and hypoid generating machines were constructed to enable a tool together with its relative motions to represent a theoretical generating gear rolling through mesh with a work gear with a minimum number of machine axes performing controlled movements during machine operation. For example, conventional machines for performing intermittent indexing operations are often referred to as "two-axis" machines because the generating operation on individual tooth spaces requires only a single timed relationship between two of the machines moveable axes. The timed relationship involves rotating a tool about a machine cradle axis in a predetermined ratio with rotation of a work gear about its axis. Together, the two timed motions represent the rotation of a theoretical generating gear in mesh with the work gear. Of course, the tool is also rotated about its axis to perform its required cutting function, but the rotational speed of the tool may be selected independently of the rotational speed of the work gear or machine cradle.
Although controlled movements about only two machine axes are required to represent the motion of a theoretical generating gear rolling through mesh with a work gear, many more axes are required to appropriately position the tool with respect to the work gear to define the theoretical generating gear itself. For example, three angular settings are required to position the tool axis with respect to the cradle axis, and one other angular setting and at least three rectilinear settings are required to position the cradle axis with respect to the work gear axis.
Conventional machines for performing continuous indexing operations are referred to as "three-axis" machines because their operation requires rotation about a third axis (i.e., the tool axis) which is controlled in accordance with a second timed relationship with rotation about the work gear axis. Rotation of the tool together with the work gear defines a continuous indexing relationship which enables the much slower generating motion between rotations about the cradle axis and work gear axis to be superimposed for collectively generating all of the tooth spaces in the work gear. However, substantially all of the same axes as described for the two-axis machines are required for purposes of setup.
Additional timed relationships between machine axes, such as movements along the machine cradle axis in time with rotation of the cradle axis have been added to conventional machines in accordance with the earlier mentioned teachings involving solutions for minimizing residual errors in generated tooth surfaces. However, the basic configuration of the conventional machines for representing theoretical generating gears remained substantially unchanged for a long period of time.
Recently, the assignee of the present invention introduced a new type of bevel and hypoid gear generating machine (see U.S. Pat. No. 4,981,402 which corresponds to WO 89/01838) which is designed with a minimum number of machine axes while providing for controlling timed relationships between most if not all of the machine axes. The reduced number of machine axes requires most of the machine axes to be controlled for performing even the simplest generating operations previously requiring only one or two timed relationships between machine axes. However, the same controlled axes may be used to accommodate all of the other known timed relationships between the axes of conventional machines.
In fact, the new machine includes the minimum number of moveable machine axes (i.e., three rectilinear axes and three rotational axes) that are kinematically required to orient the tool in any desired orientation with respect to the work gear. Of course, travel restrictions along and about the new machine axes limit the region of space within which such relative orientations can take place, but the new machine axes are configured so that the region encompasses even more space than can be defined by the many more axes of a comparatively sized conventional machine.
The new machine also makes possible a virtually unlimited number of new relative motions between the tool and work gear for generating tooth surfaces in a work gear. To date, however, the new machine has only been used to control relative motions between the tool and work gear as if it were a conventional machine having a minimum number of controlled axes. In other words, although it is known to control all of the moveable axes of the new machine for the purpose of performing known generating operations with fewer total machine axes, no teachings have been available which would enable the new machine to perform any differently than a conventional machine. In fact, as explained above, there have not been any significant new motions suggested for bevel and hypoid gear generating machines in over thirty years. Moreover, for some time now it has been known to apply computer numeric controls to most of the axes of conventional machines, but there has been no teaching to suggest any benefits from controlling more of the axes of the conventional machines during operation.
Thus, the state of the art in which the present invention was made includes well known generating processes that have been long known and practiced. Modern computer techniques have been used to optimize machine setup and operation according to the known generating processes for reducing residual errors in tooth surface geometries and achieve at least marginally acceptable contact characteristics between members of work gear pairs.